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We propose a multipole representation of the Fermi-Dirac function and theFermi operator, and use this representation to develop algorithms forelectronic structure analysis of metallic systems. The new algorithm is quitesimple and efficient. Its computational cost scales logarithmically with$\beta\Delta\eps$ where $\beta$ is the inverse temperature, and $\Delta \eps$is the width of the spectrum of the discretized Hamiltonian matrix.

Multipole Representation of the Fermi Operator with Application to the Electronic Structure Analysis of Metallic Systems